Geometric Topology in Dimensions 2 and 3

By E. Moise. 1977

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Citations in the corpus

Diversity in Faces (2019, background): “We point out that although a face image is spatially transformed during rectification, facial symmetry with respect to the face mid-line is preserved according to the topological properties of the affine transformation [68].”
Smooth approximation of bi-Lipschitz orientation-preserving homeomorphisms (2011, methodology): “In particular, it was solved by Moise [26] and Bing [7] in the case d = 3 (see also the survey book [27]), while for contractible spaces of dimension d 5 the result follows from theorems of Connell [9], Bing [8], Kirby [23] and Kirby, Siebenmann and Wall [24] (for a proof see, e.”
Toric Topology (2012, methodology): “Moreover, in dimensions 3 every topological manifold has a unique smooth structure, see [166] for a proof.”
Expanding Thurston Maps (2010, background): “We first review some standard concepts and results from plane topology (see [Mo77] for general background and more details).”
Introduction to Smooth Manifolds (2002, methodology): “In fact, it follows from work of Edwin Moise [Moi77] and James Munkres [Mun60] that every topological manifold of dimension less than or equal to 3 has a smooth structure that is unique up to diffeomorphism.”
Torus Actions and their Applications in Topology and Combinatorics (2002, background): “Brown, 1964, for 3-complexes; see [101] for the modern exposition).”
Smooth quasiregular mappings with branching (2004, methodology): “Second, in dimension n = 3 we do not have to take care of the smoothness of the map g as in (2.1) outside R, for this is provided by Kiikka [7] (who ultimately relies on deep works of Moise [ 11 ] and Munkres [12]).”
Torus actions, combinatorial topology, and homological algebra (2000, methodology): “All topological 2- and 3-dimensional manifolds can be triangulated as well (for 2-manifolds this is almost obvious, for 3-manifolds see [60]).”
Foliations and the Geometry of 3-Manifolds (2007, background): “[167], Chapter 6 for a proof in the PL case.”